Discrete stochastic models for traffic flow

Abstract

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow versus density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with a maximum velocity of 1, the simplest nontrivial approximation gives the exact result. For higher velocities, the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.